You might be right.
Let y = 0
(x - 12)^3 - 7 = 0 Subtract 7 from both sides
(x - 12)^3 = 7 Take the cube root of both sides.
x - 12 = cuberoot(7) Add 12 to both sides
x = 12 + cuberoot(7)
Are the other two real or imaginary? The quickest way to find out the answer is to graph the original equation. It has the shape of something that crosses the x axis but once. So the other two roots are imaginary.
My calculator says that the real root is 13.91
The two complex ones are 11.04 +/- 1.66i which of course is not real.
